Tableau systems are very popular in AI for their simplicity and versatility. In recent papers we showed that tableau-based procedures are intrinsically ineecient, and proposed an alternative approach of building decision procedures on top of SAT decision procedure. We called this approach \SAT-based". In extensive empirical tests on the case study of modal K, a SAT-based procedure drastically o...

We present a sound and complete tableau calculus for the class of regular grammar logics. Our tableau rules use a special feature called automaton-labelled formulae, which are similar to formulae of automaton propositional dynamic logic. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. We show that the known EXPTIME upper bound for regular gr...

This paper proposes a new class of random sequences called binary primes tableau (PT) sequences that have potential applications in cryptography and communications. The PT sequence of rank p is obtained from numbers arranged in a tableau with p columns where primes are marked off until each column has at least one prime and where the column entries are added modulo 2. We also examine the dual t...

The aim of this paper is to construct a tableau decision algorithm for the modal description logic KALC with constant domains. More precisely , we present a tableau procedure that is capable of deciding, given an ALC-formula ' with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether ' is satiss-able in a model with constant domains and arbitrary...

The paper proposes a novel framework for decentralized monitoring of Linear Temporal Logic (LTL), under the situation where processes are synchronous, uniform, and fully interconnected and the formula is represented as a tableau. In the proposed framework, processes can propagate messages containing truth values of atomic formulas, compound formulas, and temporal formulas depending on the synta...

We define a translation that maps higher-order formulas provable in a classical extensional setting to semantically equivalent formulas provable in an intuitionistic intensional setting. For the classical extensional higher-order proof system we define a Henkincomplete tableau calculus. For the intuitionistic intensional higher-order proof system we give a natural deduction calculus. We prove t...

This document is a complete draft of a chapter by Rajeev Gor e on \Tableau Methods for Modal and Temporal Logics" which is part of the \Handbook of Tableau Methods", edited by M. D'Agostino, D. Gabbay, R. H ahnle and J. Posegga, to be published in 1998 by Kluwer, Dordrecht. Any comments and corrections are highly welcome. Please email me at [email protected] The latest version of this documen...

In this paper we present a prefixed analytic tableau calculus for a wide class of normal multimodal logics; the calculus can deal in a uniform way with any logic in this class. To achieve this goal, we use a prefixed tableau calculus à la Fitting, where we explicitly represent accessibility relations between worlds by means of a graph and we use the characterizing axioms as rewriting rules. Suc...

Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant context-free grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goal-directed rules. The decision procedure also provides the essential part of the bisimulation relation betwe...

In this paper we discuss results and advantages of using steepest edge column choice rules and their derivatives. We show empirically, when we utilize the steepest edge column choice rule for the tableau method, that the density crossover point at which the tableau method is more efficient than the revised method drops to 5%. This is much lower than the 72% we have seen when the tableau method ...